Page 126 - Chemical equilibria Volume 4

102 Chemical Equilibria
We shall apply the law of mass action expressed in relation to the partial
pressures at equilibrium. In order to do so, we note that:
H
P H 2 { } y
2
P HO = {HO } = 1 y− [3.103]
2
2
and that:
P CO = { OC } = x [3.104]
P CO 2 {CO 2 } 1 x−

By substituting this back into the law of mass action, we find:
−
(1 xy = K () [3.105]
)
P
)
−
(1 yx 27
This gives us the general equation for the curves, which are sets of points
of equilibrium for reaction [3R.27]:
P
K () x
y = () 27 [3.106]
( K 27 P + ) 1 x + 1

These curves (see Figure 3.17) are equilateral hyperbolas with a horizontal
asymptote and a vertical asymptote. The concavity of the branch within the
() P
square is downturned if the constant K 27 is greater than 1 and upturned if that
() P
constant is less than 1. If K 27 is equal to 1, then the hyperbola is degenerated
into a straight line, which is the main diagonal of the square.

These curves can have an axis of symmetry which is the second diagonal
of the square (Figure 3.17) as shown by the change of variables in
accordance with:

x − (1 y− )
Y = [3.107a]
2

and:
x + (1 y− )
X = [3.107b]
2